@MintyMabel you are placing the wishes and finances of this man above a newborn baby and two small children. That is a really, really shitty attitude. Why is it the OP's job to do all this? She's raising these children and she is making them available for contact. That's the extent of her job.
Because money - that’s what children prefer to spending time with their fathers.
Oh sweetie, grow up. Kiddies cost money to raise, newsflash! Daddy clearly feels he has better uses for the cash, but Daddy will just have to jog on. I appreciate that you think it's her job to pay him to see them (both in petrol costs, and in her time and labour driving them), you've expressed that view over and over now, but you see, you're wrong, and all the idiotic, misogynistic nastiness you choose to post on Mumsnet won't alter that simple fact.
Bollocks is this about the children's best interests, as you piously claim, because you are wholly disinterested in the interests of that newborn baby, who will be strapped into a car seat for hours, completely avoidably. It is NOT ideal at all for any baby to be stuck in a car seat for hours, breaks or not, and you also need to google 'cluster feeding' because you very clearly don't know what it means. All three children will have less money in their home, too, because petrol will eat some, just as he pays less because of the new gf's kids. None of that bothers you though, does it? This man is all you care about - his interests are the only ones you register as being real and existing. The kids can fuck themselves for all you care - why would money improve their Christmas? Why would a newborn deserve more from his or her days? As long as Dad is at home with the new gf that bit longer, and they have that bit more money to spend - right? ALL in the children's interests, of course!
OP has already said she accepts that it's important her children see their father, and that's why she facilitates their going and staying with the merry-go-round of women in his life, despite her well-founded anxieties on what that instability means for her children, and despite his clearly appalling behaviour. But you can't accept that, and are determined to demonise her. The evidence is not there. You are insisting it is a woman's job to make this man's life cheaper and easier, even if the children quite literally pay the costs of that, and it makes the newborn's life harder. And if she doesn't want to, you are insisting that makes her a bad mother.
The newborn isn't a dolly, but a person, just as real and important as anyone else. These children deserve to know that their dad wants to see them and can be bothered to make the effort to do so. This parent isn't a member of this man's staff, nor his mummy, and it's not her job to run around after him and spend her money on him - at all, but especially when that in turn adversely impacts her kids. Your posts are frankly disturbing in their wilful blindness to the best interests of the children here, and your wilful blindness to the very clear evidence that this mother absolutely does facilitate and support contact, even when concerned about the carousel of new people in their lives and the disruption this represents. It's really sad to read and all I can say is that I think you need to examine the man you are with, if this is familiar and that's why you are posting as bizarrely as you are.